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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/adjoints/adjoints_ex7" target="_blank">Open adjoints_ex7 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=0.0 timesolver_upper_tolerance=0.0 solution_history_type=memory
***************************************************************

Started /bigdisk/jwpeterson/software/libmesh_build/opt_real/examples/adjoints/adjoints_ex7/.libs/example-opt
Building mesh
Building system
*** Warning, This code is untested, experimental, or likely to see future API changes: ../../../include/libmesh/memory_solution_history.h, line 51, compiled Nov 11 2021 at 13:55:10 ***
*** Warning, This code is untested, experimental, or likely to see future API changes: /home/jwpeterson/software/libmesh-src/src/solvers/file_solution_history.C, line 42, compiled Nov 11 2021 at 12:13:32 ***
Initializing systems
Setting primal initial conditions
|U(0)|= 1

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=9
    n_local_nodes()=9
  n_elem()=4
    n_local_elem()=4
    n_active_elem()=4
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HeatSystem"
    Type "Implicit"
    Variables="T"
    Finite Element Types="LAGRANGE"
    Approximation Orders="FIRST"
    n_dofs()=9
    n_local_dofs()=9
    n_constrained_dofs()=8
    n_local_constrained_dofs()=8
    n_vectors()=6
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.44444
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 8
      Number of Heterogenous Constraints= 8
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

 Solving time step 0, time = 0
  Nonlinear solver converged, step 0, residual reduction 1.92322e-16 < 1e-09
|U(0.1)|= 1.11534
Advancing timestep

 Solving time step 1, time = 0.1
  Nonlinear solver converged, step 0, residual reduction 6.06335e-16 < 1e-09
|U(0.2)|= 1.31951
Advancing timestep

 Solving time step 2, time = 0.2
  Nonlinear solver converged, step 0, residual reduction 4.94024e-16 < 1e-09
|U(0.3)|= 1.57272
Advancing timestep

 Solving time step 3, time = 0.3
  Nonlinear solver converged, step 0, residual reduction 6.74271e-16 < 1e-09
|U(0.4)|= 1.85042
Advancing timestep

 Solving time step 4, time = 0.4
  Nonlinear solver converged, step 0, residual reduction 3.62467e-16 < 1e-09
|U(0.5)|= 2.13937
Advancing timestep

 Solving time step 5, time = 0.5
  Nonlinear solver converged, step 0, residual reduction 4.81823e-16 < 1e-09
|U(0.6)|= 2.43246
Advancing timestep

 Solving time step 6, time = 0.6
  Nonlinear solver converged, step 0, residual reduction 1.14007e-15 < 1e-09
|U(0.7)|= 2.72574
Advancing timestep

 Solving time step 7, time = 0.7
  Nonlinear solver converged, step 0, residual reduction 1.3305e-15 < 1e-09
|U(0.8)|= 3.01691
Advancing timestep

 Solving time step 8, time = 0.8
  Nonlinear solver converged, step 0, residual reduction 5.5389e-16 < 1e-09
|U(0.9)|= 3.30459
Advancing timestep

 Solving time step 9, time = 0.9
  Nonlinear solver converged, step 0, residual reduction 4.03694e-16 < 1e-09
|U(1)|= 3.58796
Advancing timestep

The computed QoI 0 is 0.14948572533882531
The computed QoI 1 is 1.2818447775489428

Solving the adjoint problems.
Setting adjoint initial conditions Z(0.99999999999999989)
|Z0(0.99999999999999989)|= 1

|Z1(0.99999999999999989)|= 0

 Solving adjoint time step 0, time = 0.99999999999999989
|U(0.99999999999999989)|= 3.5879568784318079
|U(0.89999999999999991)|= 3.304592434427954
Saving adjoint and retrieving primal solutions at time t=0.89999999999999991
|Z0(0.89999999999999991)|= 1.7026879767526326

|Z1(0.89999999999999991)|= 0.17026879767526332

 Solving adjoint time step 1, time = 0.89999999999999991
|U(0.89999999999999991)|= 3.304592434427954
|U(0.79999999999999993)|= 3.0169068242592227
Saving adjoint and retrieving primal solutions at time t=0.79999999999999993
|Z0(0.79999999999999993)|= 0.77310569231412674

|Z1(0.79999999999999993)|= 0.24757936690667612

 Solving adjoint time step 2, time = 0.79999999999999993
|U(0.79999999999999993)|= 3.0169068242592227
|U(0.69999999999999996)|= 2.7257402341077488
Saving adjoint and retrieving primal solutions at time t=0.69999999999999996
|Z0(0.69999999999999996)|= 0.35102873788327599

|Z1(0.69999999999999996)|= 0.28268224069500392

 Solving adjoint time step 3, time = 0.69999999999999996
|U(0.69999999999999996)|= 2.7257402341077488
|U(0.59999999999999998)|= 2.4324649107462188
Saving adjoint and retrieving primal solutions at time t=0.59999999999999998
|Z0(0.59999999999999998)|= 0.15938464306360153

|Z1(0.59999999999999998)|= 0.29862070500136412

 Solving adjoint time step 4, time = 0.59999999999999998
|U(0.59999999999999998)|= 2.4324649107462188
|U(0.5)|= 2.1393723617401141
Saving adjoint and retrieving primal solutions at time t=0.5
|Z0(0.5)|= 0.072368617446241137

|Z1(0.5)|= 0.30585756674598796

 Solving adjoint time step 5, time = 0.5
|U(0.5)|= 2.1393723617401141
|U(0.40000000000000002)|= 1.8504189990258433
Saving adjoint and retrieving primal solutions at time t=0.40000000000000002
|Z0(0.40000000000000002)|= 0.032858979951980179

|Z1(0.40000000000000002)|= 0.30914346474118609

 Solving adjoint time step 6, time = 0.40000000000000002
|U(0.40000000000000002)|= 1.8504189990258433
|U(0.30000000000000004)|= 1.5727162358801128
Saving adjoint and retrieving primal solutions at time t=0.30000000000000004
|Z0(0.30000000000000004)|= 0.014919624024691332

|Z1(0.30000000000000004)|= 0.31063542714365516

 Solving adjoint time step 7, time = 0.30000000000000004
|U(0.30000000000000004)|= 1.5727162358801128
|U(0.20000000000000007)|= 1.3195053084916915
Saving adjoint and retrieving primal solutions at time t=0.20000000000000001
|Z0(0.20000000000000001)|= 0.0067742571852031077

|Z1(0.20000000000000001)|= 0.31131285286217547

 Solving adjoint time step 8, time = 0.20000000000000001
|U(0.20000000000000001)|= 1.3195053084916915
|U(0.099999999999999978)|= 1.1153357037209151
Saving adjoint and retrieving primal solutions at time t=0.10000000000000001
|Z0(0.10000000000000001)|= 0.0030758523361801263

|Z1(0.10000000000000001)|= 0.31162043809579359

 Solving adjoint time step 9, time = 0.10000000000000001
|U(0.10000000000000001)|= 1.1153357037209151
|U(0)|= 1
Saving adjoint and retrieving primal solutions at time t=0
|Z0(0)|= 0.0013965911442881057

|Z1(0)|= 0.31176009721022241

Computing the error estimate using the Adjoint Refinement Error Estimator

Retrieved, time = 0
|U(0)|= 1
|U_old(0)|= 0
|Z0(0)|= 0.0013965911442881057

|Z1(0)|= 0.31176009721022241

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.10000000000000001
|U(0.10000000000000001)|= 1.1153357037209151
|U_old(0.10000000000000001)|= 1
|Z0(0.10000000000000001)|= 0.0030758523361801263

|Z1(0.10000000000000001)|= 0.31162043809579359

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.20000000000000001
|U(0.20000000000000001)|= 1.3195053084916915
|U_old(0.20000000000000001)|= 1.1153357037209151
|Z0(0.20000000000000001)|= 0.0067742571852031077

|Z1(0.20000000000000001)|= 0.31131285286217547

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.30000000000000004
|U(0.30000000000000004)|= 1.5727162358801128
|U_old(0.30000000000000004)|= 1.3195053084916915
|Z0(0.30000000000000004)|= 0.014919624024691332

|Z1(0.30000000000000004)|= 0.31063542714365516

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.40000000000000002
|U(0.40000000000000002)|= 1.8504189990258433
|U_old(0.40000000000000002)|= 1.5727162358801128
|Z0(0.40000000000000002)|= 0.032858979951980179

|Z1(0.40000000000000002)|= 0.30914346474118609

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.5
|U(0.5)|= 2.1393723617401141
|U_old(0.5)|= 1.8504189990258433
|Z0(0.5)|= 0.072368617446241137

|Z1(0.5)|= 0.30585756674598796

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.59999999999999998
|U(0.59999999999999998)|= 2.4324649107462188
|U_old(0.59999999999999998)|= 2.1393723617401141
|Z0(0.59999999999999998)|= 0.15938464306360153

|Z1(0.59999999999999998)|= 0.29862070500136412

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.69999999999999996
|U(0.69999999999999996)|= 2.7257402341077488
|U_old(0.69999999999999996)|= 2.4324649107462188
|Z0(0.69999999999999996)|= 0.35102873788327599

|Z1(0.69999999999999996)|= 0.28268224069500392

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.79999999999999993
|U(0.79999999999999993)|= 3.0169068242592227
|U_old(0.79999999999999993)|= 2.7257402341077488
|Z0(0.79999999999999993)|= 0.77310569231412674

|Z1(0.79999999999999993)|= 0.24757936690667612

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.89999999999999991
|U(0.89999999999999991)|= 3.304592434427954
|U_old(0.89999999999999991)|= 3.0169068242592227
|Z0(0.89999999999999991)|= 1.7026879767526326

|Z1(0.89999999999999991)|= 0.17026879767526332

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.99999999999999989
|U(0.99999999999999989)|= 3.5879568784318079
|U_old(0.99999999999999989)|= 3.304592434427954
|Z0(0.99999999999999989)|= 1

|Z1(0.99999999999999989)|= 0

Time integrated error estimate for QoI 0: -0.44809323880671958
Time integrated error estimate for QoI 1: -0.23895256319278346

 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 13:55:23 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 ----------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.063704, Active time=0.035961                                                       |
 ----------------------------------------------------------------------------------------------------------------------
| Event                                   nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                                    w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|----------------------------------------------------------------------------------------------------------------------|
|                                                                                                                      |
|                                                                                                                      |
| DefaultCoupling                                                                                                      |
|   operator()                            4          0.0000      0.000001    0.0000      0.000001    0.02     0.02     |
|                                                                                                                      |
| DofMap                                                                                                               |
|   add_neighbors_to_send_list()          1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_constraint_matrix()             240        0.0001      0.000000    0.0001      0.000000    0.33     0.33     |
|   build_sparsity()                      1          0.0000      0.000022    0.0000      0.000029    0.06     0.08     |
|   cnstrn_elem_mat_vec()                 40         0.0019      0.000049    0.0019      0.000049    5.41     5.41     |
|   constrain_elem_matrix()               40         0.0000      0.000001    0.0000      0.000001    0.13     0.13     |
|   constrain_elem_vector()               120        0.0000      0.000000    0.0000      0.000000    0.11     0.11     |
|   create_dof_constraints()              1          0.0001      0.000110    0.0001      0.000116    0.31     0.32     |
|   distribute_dofs()                     1          0.0000      0.000015    0.0000      0.000040    0.04     0.11     |
|   dof_indices()                         1564       0.0003      0.000000    0.0003      0.000000    0.81     0.81     |
|   enforce_adjoint_constraints_exactly() 58         0.0002      0.000003    0.0002      0.000003    0.43     0.43     |
|   enforce_constraints_exactly()         32         0.0006      0.000020    0.0006      0.000020    1.76     1.76     |
|   prepare_send_list()                   2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                              1          0.0000      0.000025    0.0000      0.000025    0.07     0.07     |
|                                                                                                                      |
| EquationSystems                                                                                                      |
|   read()                                33         0.0002      0.000006    0.0002      0.000006    0.55     0.55     |
|   update()                              33         0.0000      0.000001    0.0000      0.000001    0.09     0.09     |
|   write()                               22         0.0118      0.000534    0.0118      0.000534    32.69    32.69    |
|                                                                                                                      |
| FE                                                                                                                   |
|   compute_shape_functions()             856        0.0027      0.000003    0.0027      0.000003    7.42     7.42     |
|   init_shape_functions()                214        0.0017      0.000008    0.0017      0.000008    4.71     4.71     |
|                                                                                                                      |
| FEMSystem                                                                                                            |
|   assemble_qoi()                        20         0.0005      0.000023    0.0016      0.000081    1.29     4.49     |
|   assemble_qoi_derivative()             10         0.0004      0.000044    0.0011      0.000107    1.22     2.97     |
|   assembly()                            10         0.0008      0.000075    0.0033      0.000334    2.09     9.30     |
|   assembly(get_jacobian)                10         0.0008      0.000077    0.0015      0.000148    2.15     4.13     |
|   assembly(get_residual)                67         0.0029      0.000043    0.0069      0.000103    7.97     19.11    |
|                                                                                                                      |
| FEMap                                                                                                                |
|   compute_affine_map()                  856        0.0011      0.000001    0.0011      0.000001    3.19     3.19     |
|   init_reference_to_physical_map()      214        0.0018      0.000008    0.0018      0.000008    5.03     5.03     |
|   inverse_map()                         133        0.0001      0.000000    0.0001      0.000000    0.18     0.18     |
|                                                                                                                      |
| GenericProjector                                                                                                     |
|   project                               2          0.0001      0.000043    0.0001      0.000053    0.24     0.29     |
|   project_edges                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_interiors                     2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_sides                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_vertices                      2          0.0000      0.000008    0.0000      0.000010    0.05     0.06     |
|                                                                                                                      |
| ImplicitSystem                                                                                                       |
|   adjoint_solve()                       10         0.0001      0.000007    0.0032      0.000324    0.20     9.01     |
|                                                                                                                      |
| Mesh                                                                                                                 |
|   find_neighbors()                      1          0.0000      0.000032    0.0000      0.000032    0.09     0.09     |
|   renumber_nodes_and_elem()             2          0.0000      0.000002    0.0000      0.000002    0.01     0.01     |
|                                                                                                                      |
| MeshBase                                                                                                             |
|   prepare_for_use()                     1          0.0000      0.000018    0.0001      0.000060    0.05     0.17     |
|                                                                                                                      |
| MeshCommunication                                                                                                    |
|   assign_global_indices()               55         0.0036      0.000065    0.0036      0.000065    9.97     9.97     |
|                                                                                                                      |
| MeshTools::Generation                                                                                                |
|   build_cube()                          1          0.0000      0.000044    0.0001      0.000104    0.12     0.29     |
|                                                                                                                      |
| NewtonSolver                                                                                                         |
|   solve()                               10         0.0003      0.000034    0.0057      0.000565    0.94     15.72    |
|                                                                                                                      |
| Partitioner                                                                                                          |
|   single_partition_range()              1          0.0000      0.000005    0.0000      0.000005    0.01     0.01     |
|                                                                                                                      |
| PetscLinearSolver                                                                                                    |
|   solve()                               30         0.0009      0.000030    0.0009      0.000030    2.52     2.52     |
|                                                                                                                      |
| System                                                                                                               |
|   calculate_norm()                      97         0.0027      0.000028    0.0035      0.000036    7.60     9.60     |
|   project_fem_vector()                  2          0.0001      0.000026    0.0002      0.000102    0.14     0.56     |
|   project_vector(FunctionBase)          2          0.0000      0.000000    0.0002      0.000102    0.00     0.57     |
 ----------------------------------------------------------------------------------------------------------------------
| Totals:                                 4805       0.0360                                          100.00            |
 ----------------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=0.0 timesolver_upper_tolerance=0.0 solution_history_type=memory
***************************************************************
***************************************************************
* Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=0.0 timesolver_upper_tolerance=0.0 solution_history_type=file
***************************************************************

Started /bigdisk/jwpeterson/software/libmesh_build/opt_real/examples/adjoints/adjoints_ex7/.libs/example-opt
Building mesh
Building system
*** Warning, This code is untested, experimental, or likely to see future API changes: /home/jwpeterson/software/libmesh-src/src/solvers/file_solution_history.C, line 42, compiled Nov 11 2021 at 12:13:32 ***
Initializing systems
Setting primal initial conditions
|U(0)|= 1

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=9
    n_local_nodes()=9
  n_elem()=4
    n_local_elem()=4
    n_active_elem()=4
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HeatSystem"
    Type "Implicit"
    Variables="T"
    Finite Element Types="LAGRANGE"
    Approximation Orders="FIRST"
    n_dofs()=9
    n_local_dofs()=9
    n_constrained_dofs()=8
    n_local_constrained_dofs()=8
    n_vectors()=6
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.44444
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 8
      Number of Heterogenous Constraints= 8
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

 Solving time step 0, time = 0
  Nonlinear solver converged, step 0, residual reduction 1.92322e-16 < 1e-09
|U(0.1)|= 1.11534
Advancing timestep

 Solving time step 1, time = 0.1
  Nonlinear solver converged, step 0, residual reduction 6.06335e-16 < 1e-09
|U(0.2)|= 1.31951
Advancing timestep

 Solving time step 2, time = 0.2
  Nonlinear solver converged, step 0, residual reduction 4.94024e-16 < 1e-09
|U(0.3)|= 1.57272
Advancing timestep

 Solving time step 3, time = 0.3
  Nonlinear solver converged, step 0, residual reduction 6.74271e-16 < 1e-09
|U(0.4)|= 1.85042
Advancing timestep

 Solving time step 4, time = 0.4
  Nonlinear solver converged, step 0, residual reduction 3.62467e-16 < 1e-09
|U(0.5)|= 2.13937
Advancing timestep

 Solving time step 5, time = 0.5
  Nonlinear solver converged, step 0, residual reduction 4.81823e-16 < 1e-09
|U(0.6)|= 2.43246
Advancing timestep

 Solving time step 6, time = 0.6
  Nonlinear solver converged, step 0, residual reduction 1.14007e-15 < 1e-09
|U(0.7)|= 2.72574
Advancing timestep

 Solving time step 7, time = 0.7
  Nonlinear solver converged, step 0, residual reduction 1.3305e-15 < 1e-09
|U(0.8)|= 3.01691
Advancing timestep

 Solving time step 8, time = 0.8
  Nonlinear solver converged, step 0, residual reduction 5.5389e-16 < 1e-09
|U(0.9)|= 3.30459
Advancing timestep

 Solving time step 9, time = 0.9
  Nonlinear solver converged, step 0, residual reduction 4.03694e-16 < 1e-09
|U(1)|= 3.58796
Advancing timestep

The computed QoI 0 is 0.14948572533882531
The computed QoI 1 is 1.2818447775489428

Solving the adjoint problems.
Setting adjoint initial conditions Z(0.99999999999999989)
|Z0(0.99999999999999989)|= 1

|Z1(0.99999999999999989)|= 0

 Solving adjoint time step 0, time = 0.99999999999999989
|U(0.99999999999999989)|= 3.5879568784318079
|U(0.89999999999999991)|= 3.304592434427954
Saving adjoint and retrieving primal solutions at time t=0.89999999999999991
|Z0(0.89999999999999991)|= 1.7026879767526326

|Z1(0.89999999999999991)|= 0.17026879767526332

 Solving adjoint time step 1, time = 0.89999999999999991
|U(0.89999999999999991)|= 3.304592434427954
|U(0.79999999999999993)|= 3.0169068242592227
Saving adjoint and retrieving primal solutions at time t=0.79999999999999993
|Z0(0.79999999999999993)|= 0.77310569231412674

|Z1(0.79999999999999993)|= 0.24757936690667612

 Solving adjoint time step 2, time = 0.79999999999999993
|U(0.79999999999999993)|= 3.0169068242592227
|U(0.69999999999999996)|= 2.7257402341077488
Saving adjoint and retrieving primal solutions at time t=0.69999999999999996
|Z0(0.69999999999999996)|= 0.35102873788327599

|Z1(0.69999999999999996)|= 0.28268224069500392

 Solving adjoint time step 3, time = 0.69999999999999996
|U(0.69999999999999996)|= 2.7257402341077488
|U(0.59999999999999998)|= 2.4324649107462188
Saving adjoint and retrieving primal solutions at time t=0.59999999999999998
|Z0(0.59999999999999998)|= 0.15938464306360153

|Z1(0.59999999999999998)|= 0.29862070500136412

 Solving adjoint time step 4, time = 0.59999999999999998
|U(0.59999999999999998)|= 2.4324649107462188
|U(0.5)|= 2.1393723617401141
Saving adjoint and retrieving primal solutions at time t=0.5
|Z0(0.5)|= 0.072368617446241137

|Z1(0.5)|= 0.30585756674598796

 Solving adjoint time step 5, time = 0.5
|U(0.5)|= 2.1393723617401141
|U(0.40000000000000002)|= 1.8504189990258433
Saving adjoint and retrieving primal solutions at time t=0.40000000000000002
|Z0(0.40000000000000002)|= 0.032858979951980179

|Z1(0.40000000000000002)|= 0.30914346474118609

 Solving adjoint time step 6, time = 0.40000000000000002
|U(0.40000000000000002)|= 1.8504189990258433
|U(0.30000000000000004)|= 1.5727162358801128
Saving adjoint and retrieving primal solutions at time t=0.30000000000000004
|Z0(0.30000000000000004)|= 0.014919624024691332

|Z1(0.30000000000000004)|= 0.31063542714365516

 Solving adjoint time step 7, time = 0.30000000000000004
|U(0.30000000000000004)|= 1.5727162358801128
|U(0.20000000000000007)|= 1.3195053084916915
Saving adjoint and retrieving primal solutions at time t=0.20000000000000001
|Z0(0.20000000000000001)|= 0.0067742571852031077

|Z1(0.20000000000000001)|= 0.31131285286217547

 Solving adjoint time step 8, time = 0.20000000000000001
|U(0.20000000000000001)|= 1.3195053084916915
|U(0.099999999999999978)|= 1.1153357037209151
Saving adjoint and retrieving primal solutions at time t=0.10000000000000001
|Z0(0.10000000000000001)|= 0.0030758523361801263

|Z1(0.10000000000000001)|= 0.31162043809579359

 Solving adjoint time step 9, time = 0.10000000000000001
|U(0.10000000000000001)|= 1.1153357037209151
|U(0)|= 1
Saving adjoint and retrieving primal solutions at time t=0
|Z0(0)|= 0.0013965911442881057

|Z1(0)|= 0.31176009721022241

Computing the error estimate using the Adjoint Refinement Error Estimator

Retrieved, time = 0
|U(0)|= 1
|U_old(0)|= 0
|Z0(0)|= 0.0013965911442881057

|Z1(0)|= 0.31176009721022241

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.10000000000000001
|U(0.10000000000000001)|= 1.1153357037209151
|U_old(0.10000000000000001)|= 1
|Z0(0.10000000000000001)|= 0.0030758523361801263

|Z1(0.10000000000000001)|= 0.31162043809579359

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.20000000000000001
|U(0.20000000000000001)|= 1.3195053084916915
|U_old(0.20000000000000001)|= 1.1153357037209151
|Z0(0.20000000000000001)|= 0.0067742571852031077

|Z1(0.20000000000000001)|= 0.31131285286217547

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.30000000000000004
|U(0.30000000000000004)|= 1.5727162358801128
|U_old(0.30000000000000004)|= 1.3195053084916915
|Z0(0.30000000000000004)|= 0.014919624024691332

|Z1(0.30000000000000004)|= 0.31063542714365516

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.40000000000000002
|U(0.40000000000000002)|= 1.8504189990258433
|U_old(0.40000000000000002)|= 1.5727162358801128
|Z0(0.40000000000000002)|= 0.032858979951980179

|Z1(0.40000000000000002)|= 0.30914346474118609

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.5
|U(0.5)|= 2.1393723617401141
|U_old(0.5)|= 1.8504189990258433
|Z0(0.5)|= 0.072368617446241137

|Z1(0.5)|= 0.30585756674598796

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.59999999999999998
|U(0.59999999999999998)|= 2.4324649107462188
|U_old(0.59999999999999998)|= 2.1393723617401141
|Z0(0.59999999999999998)|= 0.15938464306360153

|Z1(0.59999999999999998)|= 0.29862070500136412

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.69999999999999996
|U(0.69999999999999996)|= 2.7257402341077488
|U_old(0.69999999999999996)|= 2.4324649107462188
|Z0(0.69999999999999996)|= 0.35102873788327599

|Z1(0.69999999999999996)|= 0.28268224069500392

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.79999999999999993
|U(0.79999999999999993)|= 3.0169068242592227
|U_old(0.79999999999999993)|= 2.7257402341077488
|Z0(0.79999999999999993)|= 0.77310569231412674

|Z1(0.79999999999999993)|= 0.24757936690667612

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.89999999999999991
|U(0.89999999999999991)|= 3.304592434427954
|U_old(0.89999999999999991)|= 3.0169068242592227
|Z0(0.89999999999999991)|= 1.7026879767526326

|Z1(0.89999999999999991)|= 0.17026879767526332

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.99999999999999989
|U(0.99999999999999989)|= 3.5879568784318079
|U_old(0.99999999999999989)|= 3.304592434427954
|Z0(0.99999999999999989)|= 1

|Z1(0.99999999999999989)|= 0

Time integrated error estimate for QoI 0: -0.44809323880671958
Time integrated error estimate for QoI 1: -0.23895256319278346

 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 13:55:23 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 ----------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.066309, Active time=0.037697                                                       |
 ----------------------------------------------------------------------------------------------------------------------
| Event                                   nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                                    w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|----------------------------------------------------------------------------------------------------------------------|
|                                                                                                                      |
|                                                                                                                      |
| DefaultCoupling                                                                                                      |
|   operator()                            4          0.0000      0.000001    0.0000      0.000001    0.01     0.01     |
|                                                                                                                      |
| DofMap                                                                                                               |
|   add_neighbors_to_send_list()          1          0.0000      0.000001    0.0000      0.000001    0.00     0.00     |
|   build_constraint_matrix()             240        0.0001      0.000000    0.0001      0.000000    0.27     0.27     |
|   build_sparsity()                      1          0.0000      0.000024    0.0000      0.000029    0.06     0.08     |
|   cnstrn_elem_mat_vec()                 40         0.0020      0.000050    0.0020      0.000050    5.29     5.29     |
|   constrain_elem_matrix()               40         0.0001      0.000001    0.0001      0.000001    0.14     0.14     |
|   constrain_elem_vector()               120        0.0000      0.000000    0.0000      0.000000    0.12     0.12     |
|   create_dof_constraints()              1          0.0001      0.000128    0.0001      0.000136    0.34     0.36     |
|   distribute_dofs()                     1          0.0000      0.000013    0.0000      0.000039    0.03     0.10     |
|   dof_indices()                         1564       0.0003      0.000000    0.0003      0.000000    0.80     0.80     |
|   enforce_adjoint_constraints_exactly() 58         0.0002      0.000003    0.0002      0.000003    0.41     0.41     |
|   enforce_constraints_exactly()         32         0.0006      0.000020    0.0006      0.000020    1.72     1.72     |
|   prepare_send_list()                   2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                              1          0.0000      0.000025    0.0000      0.000025    0.07     0.07     |
|                                                                                                                      |
| EquationSystems                                                                                                      |
|   read()                                33         0.0002      0.000006    0.0002      0.000006    0.54     0.54     |
|   update()                              33         0.0000      0.000001    0.0000      0.000001    0.09     0.09     |
|   write()                               22         0.0132      0.000601    0.0132      0.000601    35.08    35.08    |
|                                                                                                                      |
| FE                                                                                                                   |
|   compute_shape_functions()             856        0.0027      0.000003    0.0027      0.000003    7.17     7.17     |
|   init_shape_functions()                214        0.0017      0.000008    0.0017      0.000008    4.56     4.56     |
|                                                                                                                      |
| FEMSystem                                                                                                            |
|   assemble_qoi()                        20         0.0005      0.000024    0.0017      0.000083    1.27     4.40     |
|   assemble_qoi_derivative()             10         0.0004      0.000044    0.0011      0.000107    1.16     2.85     |
|   assembly()                            10         0.0008      0.000077    0.0034      0.000344    2.05     9.14     |
|   assembly(get_jacobian)                10         0.0008      0.000076    0.0014      0.000143    2.02     3.79     |
|   assembly(get_residual)                67         0.0029      0.000044    0.0070      0.000105    7.75     18.68    |
|                                                                                                                      |
| FEMap                                                                                                                |
|   compute_affine_map()                  856        0.0012      0.000001    0.0012      0.000001    3.15     3.15     |
|   init_reference_to_physical_map()      214        0.0018      0.000009    0.0018      0.000009    4.84     4.84     |
|   inverse_map()                         133        0.0001      0.000000    0.0001      0.000000    0.17     0.17     |
|                                                                                                                      |
| GenericProjector                                                                                                     |
|   project                               2          0.0001      0.000041    0.0001      0.000051    0.21     0.27     |
|   project_edges                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_interiors                     2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_sides                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_vertices                      2          0.0000      0.000006    0.0000      0.000010    0.03     0.05     |
|                                                                                                                      |
| ImplicitSystem                                                                                                       |
|   adjoint_solve()                       10         0.0001      0.000007    0.0032      0.000319    0.19     8.45     |
|                                                                                                                      |
| Mesh                                                                                                                 |
|   find_neighbors()                      1          0.0000      0.000037    0.0000      0.000037    0.10     0.10     |
|   renumber_nodes_and_elem()             2          0.0000      0.000002    0.0000      0.000002    0.01     0.01     |
|                                                                                                                      |
| MeshBase                                                                                                             |
|   prepare_for_use()                     1          0.0000      0.000019    0.0001      0.000061    0.05     0.16     |
|                                                                                                                      |
| MeshCommunication                                                                                                    |
|   assign_global_indices()               55         0.0035      0.000064    0.0035      0.000064    9.29     9.29     |
|                                                                                                                      |
| MeshTools::Generation                                                                                                |
|   build_cube()                          1          0.0000      0.000040    0.0001      0.000101    0.11     0.27     |
|                                                                                                                      |
| NewtonSolver                                                                                                         |
|   solve()                               10         0.0003      0.000034    0.0058      0.000580    0.91     15.39    |
|                                                                                                                      |
| Partitioner                                                                                                          |
|   single_partition_range()              1          0.0000      0.000001    0.0000      0.000001    0.00     0.00     |
|                                                                                                                      |
| PetscLinearSolver                                                                                                    |
|   solve()                               30         0.0009      0.000031    0.0009      0.000031    2.44     2.44     |
|                                                                                                                      |
| System                                                                                                               |
|   calculate_norm()                      97         0.0028      0.000029    0.0035      0.000036    7.37     9.22     |
|   project_fem_vector()                  2          0.0001      0.000027    0.0002      0.000100    0.14     0.53     |
|   project_vector(FunctionBase)          2          0.0000      0.000000    0.0002      0.000100    0.00     0.53     |
 ----------------------------------------------------------------------------------------------------------------------
| Totals:                                 4805       0.0377                                          100.00            |
 ----------------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=0.0 timesolver_upper_tolerance=0.0 solution_history_type=file
***************************************************************
***************************************************************
* Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=1.0 timesolver_upper_tolerance=1.2 solution_history_type=memory
***************************************************************

Started /bigdisk/jwpeterson/software/libmesh_build/opt_real/examples/adjoints/adjoints_ex7/.libs/example-opt
Building mesh
Building system
*** Warning, This code is untested, experimental, or likely to see future API changes: ../../../include/libmesh/memory_solution_history.h, line 51, compiled Nov 11 2021 at 13:55:10 ***
Initializing systems
Setting primal initial conditions
|U(0)|= 1

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=9
    n_local_nodes()=9
  n_elem()=4
    n_local_elem()=4
    n_active_elem()=4
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HeatSystem"
    Type "Implicit"
    Variables="T"
    Finite Element Types="LAGRANGE"
    Approximation Orders="FIRST"
    n_dofs()=9
    n_local_dofs()=9
    n_constrained_dofs()=8
    n_local_constrained_dofs()=8
    n_vectors()=6
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.44444
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 8
      Number of Heterogenous Constraints= 8
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

 Solving time step 0, time = 0

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.92322e-16 < 1e-09
Double norm = 3.08022
  Nonlinear solver converged, step 0, residual reduction 8.93858e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 8.28397e-16 < 1e-09
Single norm = 3.08073
Error norm = 0.00128728
Local relative error = 0.000417849
Global relative error = 0.00417849
old delta t = 0.1
The global growth/shrink factor is: 239.321
The local growth/shrink factor is: 48.9204
delta t is constrained by max_growth
new delta t = 0.112
|U(0.1)|= 1.11633
Advancing timestep

 Solving time step 1, time = 0.1

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 7.10284e-16 < 1e-09
Double norm = 3.18331
  Nonlinear solver converged, step 0, residual reduction 1.26636e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 8.84037e-16 < 1e-09
Single norm = 3.18403
Error norm = 0.00156781
Local relative error = 0.000492398
Global relative error = 0.00439641
old delta t = 0.112
The global growth/shrink factor is: 227.458
The local growth/shrink factor is: 45.0653
delta t is constrained by max_growth
new delta t = 0.12544
|U(0.212)|= 1.35075
Advancing timestep

 Solving time step 2, time = 0.212

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 6.02586e-16 < 1e-09
Double norm = 3.31174
  Nonlinear solver converged, step 0, residual reduction 6.69829e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 2.36797e-16 < 1e-09
Single norm = 3.31273
Error norm = 0.00190279
Local relative error = 0.000574385
Global relative error = 0.00457897
old delta t = 0.12544
The global growth/shrink factor is: 218.39
The local growth/shrink factor is: 41.7252
delta t is constrained by max_growth
new delta t = 0.140493
|U(0.33744)|= 1.67949
Advancing timestep

 Solving time step 3, time = 0.33744

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 4.55856e-17 < 1e-09
Double norm = 3.468
  Nonlinear solver converged, step 0, residual reduction 8.46901e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 9.05589e-16 < 1e-09
Single norm = 3.46933
Error norm = 0.0023003
Local relative error = 0.000663037
Global relative error = 0.00471937
old delta t = 0.140493
The global growth/shrink factor is: 211.893
The local growth/shrink factor is: 38.8357
delta t is constrained by max_growth
new delta t = 0.157352
|U(0.477933)|= 2.08154
Advancing timestep

 Solving time step 4, time = 0.477933

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 5.06191e-16 < 1e-09
Double norm = 3.65407
  Nonlinear solver converged, step 0, residual reduction 6.13537e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 3.55934e-16 < 1e-09
Single norm = 3.65582
Error norm = 0.0027687
Local relative error = 0.000757338
Global relative error = 0.00481302
old delta t = 0.157352
The global growth/shrink factor is: 207.77
The local growth/shrink factor is: 36.3375
delta t is constrained by max_growth
new delta t = 0.176234
|U(0.635285)|= 2.54376
Advancing timestep

 Solving time step 5, time = 0.635285

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 9.4768e-16 < 1e-09
Double norm = 3.87129
  Nonlinear solver converged, step 0, residual reduction 1.05274e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 1.0905e-15 < 1e-09
Single norm = 3.87356
Error norm = 0.00331621
Local relative error = 0.000856113
Global relative error = 0.00485782
old delta t = 0.176234
The global growth/shrink factor is: 205.854
The local growth/shrink factor is: 34.177
delta t is constrained by max_growth
new delta t = 0.197382
|U(0.811519)|= 3.05853
Advancing timestep

 Solving time step 6, time = 0.811519

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 4.65092e-16 < 1e-09
Double norm = 4.1203
  Nonlinear solver converged, step 0, residual reduction 4.79933e-17 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 6.53988e-16 < 1e-09
Single norm = 4.12317
Error norm = 0.00395034
Local relative error = 0.000958082
Global relative error = 0.00485394
old delta t = 0.197382
The global growth/shrink factor is: 206.018
The local growth/shrink factor is: 32.3072
delta t is constrained by max_growth
new delta t = 0.221068
|U(1.0089)|= 3.62108
Advancing timestep

 Solving time step 7, time = 1.0089

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.58181e-16 < 1e-09
Double norm = 4.40092
  Nonlinear solver converged, step 0, residual reduction 3.20932e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 1.44936e-16 < 1e-09
Single norm = 4.40451
Error norm = 0.00467711
Local relative error = 0.00106189
Global relative error = 0.00480346
old delta t = 0.221068
The global growth/shrink factor is: 208.183
The local growth/shrink factor is: 30.6874
delta t is constrained by max_growth
new delta t = 0.247596
|U(1.22997)|= 4.2278
Advancing timestep

 Solving time step 8, time = 1.22997

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.69811e-16 < 1e-09
Double norm = 4.71218
  Nonlinear solver converged, step 0, residual reduction 4.94396e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 6.144e-16 < 1e-09
Single norm = 4.71658
Error norm = 0.00550003
Local relative error = 0.00116611
Global relative error = 0.00470971
old delta t = 0.247596
The global growth/shrink factor is: 212.327
The local growth/shrink factor is: 29.284
delta t is constrained by max_growth
new delta t = 0.277308
|U(1.47757)|= 4.8753
Advancing timestep

 Solving time step 9, time = 1.47757

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 7.55333e-16 < 1e-09
Double norm = 5.05222
  Nonlinear solver converged, step 0, residual reduction 7.59955e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 2.75131e-16 < 1e-09
Single norm = 5.05754
Error norm = 0.0064188
Local relative error = 0.00126915
Global relative error = 0.0045767
old delta t = 0.277308
The global growth/shrink factor is: 218.498
The local growth/shrink factor is: 28.07
delta t is constrained by max_growth
new delta t = 0.310585
|U(1.75487)|= 5.55978
Advancing timestep

The computed QoI 0 is 0.24932406066164053
The computed QoI 1 is 2.5421286435672119

Solving the adjoint problems.
Setting adjoint initial conditions Z(1.7548735069535084)
|Z0(1.7548735069535084)|= 1

|Z1(1.7548735069535084)|= 0

 Solving adjoint time step 0, time = 1.7548735069535084
|U(1.7548735069535084)|= 5.5597817470095023
|U(1.6162195690809991)|= 5.2227225913862583
Saving adjoint and retrieving primal solutions at time t=1.6162195690809991
|Z0(1.4775656312084897)|= 0.52714277783603058

|Z1(1.4775656312084897)|= 0.26803536445142789

 Solving adjoint time step 1, time = 1.4775656312084897
|U(1.4775656312084897)|= 4.8753000036749743
|U(1.3389116933359804)|= 4.5557169985004684
Saving adjoint and retrieving primal solutions at time t=1.3537674723937492
|Z0(1.2299693135790086)|= 0.085120829331890482

|Z1(1.2299693135790086)|= 0.30479700354857892

 Solving adjoint time step 2, time = 1.2299693135790086
|U(1.2299693135790086)|= 4.2278011018084714
|U(1.1061711547642681)|= 3.9276118455968652
Saving adjoint and retrieving primal solutions at time t=1.1194352432087045
|Z0(1.0089011728384003)|= 0.015691840061529811

|Z1(1.0089011728384003)|= 0.3105712042530332

 Solving adjoint time step 3, time = 1.0089011728384003
|U(1.0089011728384003)|= 3.6210787050559499
|U(0.89836710246809615)|= 3.341951147192225
Saving adjoint and retrieving primal solutions at time t=0.91021003857920024
|Z0(0.81151890432000018)|= 0.0032817876666856086

|Z1(0.81151890432000018)|= 0.31160331107229816

 Solving adjoint time step 4, time = 0.81151890432000018
|U(0.81151890432000018)|= 3.0585320644998721
|U(0.71282777006080011)|= 2.8021388853764262
Saving adjoint and retrieving primal solutions at time t=0.7234018201600001
|Z0(0.63528473600000002)|= 0.00077371056468026299

|Z1(0.63528473600000002)|= 0.31181190031897216

 Solving adjoint time step 5, time = 0.63528473600000002
|U(0.63528473600000002)|= 2.543759970717383
|U(0.54716765183999994)|= 2.3121900921206135
Saving adjoint and retrieving primal solutions at time t=0.55660876800000003
|Z0(0.47793279999999994)|= 0.00020431155391876837

|Z1(0.47793279999999994)|= 0.31185925552612093

 Solving adjoint time step 6, time = 0.47793279999999994
|U(0.47793279999999994)|= 2.0815385167141343
|U(0.39925683199999989)|= 1.8779985387409239
Saving adjoint and retrieving primal solutions at time t=0.40768639999999989
|Z0(0.33743999999999985)|= 6.0043832595599244e-05

|Z1(0.33743999999999985)|= 0.31187125383960418

 Solving adjoint time step 7, time = 0.33743999999999985
|U(0.33743999999999985)|= 1.6794923909523405
|U(0.26719359999999981)|= 1.5094758519366982
Saving adjoint and retrieving primal solutions at time t=0.27471999999999985
|Z0(0.21199999999999986)|= 1.9513594998847448e-05

|Z1(0.21199999999999986)|= 0.31187462461784737

 Solving adjoint time step 8, time = 0.21199999999999986
|U(0.21199999999999986)|= 1.350745356154194
|U(0.14927999999999986)|= 1.2234740927197323
Saving adjoint and retrieving primal solutions at time t=0.15599999999999983
|Z0(0.099999999999999811)|= 6.9689416041385094e-06

|Z1(0.099999999999999811)|= 0.3118756679190276

 Solving adjoint time step 9, time = 0.099999999999999811
|U(0.099999999999999811)|= 1.1163303097816257
|U(0.043999999999999789)|= 1.0439877643180528
Saving adjoint and retrieving primal solutions at time t=0.049999999999999808
|Z0(-1.9428902930940239e-16)|= 2.718164039090695e-06

|Z1(-1.9428902930940239e-16)|= 0.31187602144344273

Computing the error estimate using the Adjoint Refinement Error Estimator

Retrieved, time = -1.9428902930940239e-16
|U(-1.9428902930940239e-16)|= 1
|U_old(-1.9428902930940239e-16)|= 0
|Z0(-1.9428902930940239e-16)|= 2.718164039090695e-06

|Z1(-1.9428902930940239e-16)|= 0.31187602144344273

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.099999999999999811
|U(0.099999999999999811)|= 1.1163303097816257
|U_old(0.099999999999999811)|= 1.0439877643180528
|Z0(0.099999999999999811)|= 6.9689416041385094e-06

|Z1(0.099999999999999811)|= 0.3118756679190276

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.21199999999999983
|U(0.21199999999999983)|= 1.350745356154194
|U_old(0.21199999999999983)|= 1.2234740927197323
|Z0(0.21199999999999983)|= 1.9513594998847448e-05

|Z1(0.21199999999999983)|= 0.31187462461784737

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.33743999999999991
|U(0.33743999999999991)|= 1.6794923909523405
|U_old(0.33743999999999991)|= 1.5094758519366982
|Z0(0.33743999999999991)|= 6.0043832595599244e-05

|Z1(0.33743999999999991)|= 0.31187125383960418

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.47793279999999994
|U(0.47793279999999994)|= 2.0815385167141343
|U_old(0.47793279999999994)|= 1.8779985387409239
|Z0(0.47793279999999994)|= 0.00020431155391876837

|Z1(0.47793279999999994)|= 0.31185925552612093

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.63528473600000002
|U(0.63528473600000002)|= 2.543759970717383
|U_old(0.63528473600000002)|= 2.3121900921206135
|Z0(0.63528473600000002)|= 0.00077371056468026299

|Z1(0.63528473600000002)|= 0.31181190031897216

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.81151890432000007
|U(0.81151890432000007)|= 3.0585320644998721
|U_old(0.81151890432000007)|= 2.8021388853764262
|Z0(0.81151890432000007)|= 0.0032817876666856086

|Z1(0.81151890432000007)|= 0.31160331107229816

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.0089011728384003
|U(1.0089011728384003)|= 3.6210787050559499
|U_old(1.0089011728384003)|= 3.341951147192225
|Z0(1.0089011728384003)|= 0.015691840061529811

|Z1(1.0089011728384003)|= 0.3105712042530332

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.2299693135790084
|U(1.2299693135790084)|= 4.2278011018084714
|U_old(1.2299693135790084)|= 3.9276118455968652
|Z0(1.2299693135790084)|= 0.085120829331890482

|Z1(1.2299693135790084)|= 0.30479700354857892

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.4775656312084895
|U(1.4775656312084895)|= 4.8753000036749743
|U_old(1.4775656312084895)|= 4.5557169985004684
|Z0(1.4775656312084895)|= 0.52714277783603058

|Z1(1.4775656312084895)|= 0.26803536445142789

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.7548735069535084
|U(1.7548735069535084)|= 5.5597817470095023
|U_old(1.7548735069535084)|= 5.2227225913862583
|Z0(1.7548735069535084)|= 1

|Z1(1.7548735069535084)|= 0

Time integrated error estimate for QoI 0: -0.75139371165754232
Time integrated error estimate for QoI 1: -0.70905030091469889

 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 13:55:23 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 ----------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.050074, Active time=0.036927                                                       |
 ----------------------------------------------------------------------------------------------------------------------
| Event                                   nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                                    w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|----------------------------------------------------------------------------------------------------------------------|
|                                                                                                                      |
|                                                                                                                      |
| DefaultCoupling                                                                                                      |
|   operator()                            4          0.0000      0.000001    0.0000      0.000001    0.01     0.01     |
|                                                                                                                      |
| DofMap                                                                                                               |
|   add_neighbors_to_send_list()          1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_constraint_matrix()             560        0.0002      0.000000    0.0002      0.000000    0.60     0.60     |
|   build_sparsity()                      1          0.0000      0.000023    0.0000      0.000029    0.06     0.08     |
|   cnstrn_elem_mat_vec()                 120        0.0019      0.000016    0.0019      0.000016    5.22     5.22     |
|   constrain_elem_matrix()               80         0.0001      0.000001    0.0001      0.000001    0.21     0.21     |
|   constrain_elem_vector()               280        0.0001      0.000000    0.0001      0.000000    0.23     0.23     |
|   create_dof_constraints()              1          0.0001      0.000102    0.0001      0.000109    0.28     0.30     |
|   distribute_dofs()                     1          0.0000      0.000013    0.0000      0.000040    0.04     0.11     |
|   dof_indices()                         2844       0.0005      0.000000    0.0005      0.000000    1.35     1.35     |
|   enforce_adjoint_constraints_exactly() 118        0.0003      0.000003    0.0003      0.000003    0.81     0.81     |
|   enforce_constraints_exactly()         92         0.0016      0.000017    0.0016      0.000017    4.30     4.30     |
|   prepare_send_list()                   2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                              1          0.0000      0.000027    0.0000      0.000027    0.07     0.07     |
|                                                                                                                      |
| FE                                                                                                                   |
|   compute_shape_functions()             1416       0.0057      0.000004    0.0057      0.000004    15.45    15.45    |
|   init_shape_functions()                354        0.0034      0.000010    0.0034      0.000010    9.18     9.18     |
|                                                                                                                      |
| FEMSystem                                                                                                            |
|   assemble_qoi()                        40         0.0008      0.000019    0.0030      0.000075    2.04     8.11     |
|   assemble_qoi_derivative()             20         0.0008      0.000041    0.0022      0.000112    2.24     6.08     |
|   assembly()                            30         0.0021      0.000068    0.0059      0.000195    5.57     15.86    |
|   assembly(get_jacobian)                20         0.0014      0.000072    0.0028      0.000140    3.88     7.56     |
|   assembly(get_residual)                147        0.0059      0.000040    0.0146      0.000100    15.98    39.65    |
|                                                                                                                      |
| FEMap                                                                                                                |
|   compute_affine_map()                  1416       0.0024      0.000002    0.0024      0.000002    6.54     6.54     |
|   init_reference_to_physical_map()      354        0.0038      0.000011    0.0038      0.000011    10.18    10.18    |
|   inverse_map()                         273        0.0001      0.000000    0.0001      0.000000    0.36     0.36     |
|                                                                                                                      |
| GenericProjector                                                                                                     |
|   project                               2          0.0001      0.000041    0.0001      0.000050    0.22     0.27     |
|   project_edges                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_interiors                     2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_sides                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_vertices                      2          0.0000      0.000008    0.0000      0.000010    0.04     0.05     |
|                                                                                                                      |
| ImplicitSystem                                                                                                       |
|   adjoint_solve()                       20         0.0001      0.000006    0.0062      0.000312    0.35     16.92    |
|                                                                                                                      |
| Mesh                                                                                                                 |
|   find_neighbors()                      1          0.0000      0.000038    0.0000      0.000038    0.10     0.10     |
|   renumber_nodes_and_elem()             2          0.0000      0.000002    0.0000      0.000002    0.01     0.01     |
|                                                                                                                      |
| MeshBase                                                                                                             |
|   prepare_for_use()                     1          0.0000      0.000018    0.0001      0.000065    0.05     0.18     |
|                                                                                                                      |
| MeshTools::Generation                                                                                                |
|   build_cube()                          1          0.0000      0.000046    0.0001      0.000111    0.12     0.30     |
|                                                                                                                      |
| NewtonSolver                                                                                                         |
|   solve()                               30         0.0008      0.000027    0.0121      0.000404    2.22     32.81    |
|                                                                                                                      |
| Partitioner                                                                                                          |
|   single_partition_range()              1          0.0000      0.000004    0.0000      0.000004    0.01     0.01     |
|                                                                                                                      |
| PetscLinearSolver                                                                                                    |
|   solve()                               70         0.0018      0.000026    0.0018      0.000026    4.91     4.91     |
|                                                                                                                      |
| System                                                                                                               |
|   calculate_norm()                      127        0.0027      0.000021    0.0033      0.000026    7.20     8.92     |
|   project_fem_vector()                  2          0.0001      0.000031    0.0002      0.000105    0.17     0.57     |
|   project_vector(FunctionBase)          2          0.0000      0.000000    0.0002      0.000105    0.00     0.57     |
 ----------------------------------------------------------------------------------------------------------------------
| Totals:                                 8442       0.0369                                          100.00            |
 ----------------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=1.0 timesolver_upper_tolerance=1.2 solution_history_type=memory
***************************************************************
***************************************************************
* Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=1.0 timesolver_upper_tolerance=1.2 solution_history_type=file
***************************************************************

Started /bigdisk/jwpeterson/software/libmesh_build/opt_real/examples/adjoints/adjoints_ex7/.libs/example-opt
Building mesh
Building system
*** Warning, This code is untested, experimental, or likely to see future API changes: /home/jwpeterson/software/libmesh-src/src/solvers/file_solution_history.C, line 42, compiled Nov 11 2021 at 12:13:32 ***
Initializing systems
Setting primal initial conditions
|U(0)|= 1

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=9
    n_local_nodes()=9
  n_elem()=4
    n_local_elem()=4
    n_active_elem()=4
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "HeatSystem"
    Type "Implicit"
    Variables="T"
    Finite Element Types="LAGRANGE"
    Approximation Orders="FIRST"
    n_dofs()=9
    n_local_dofs()=9
    n_constrained_dofs()=8
    n_local_constrained_dofs()=8
    n_vectors()=6
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.44444
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 8
      Number of Heterogenous Constraints= 8
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

 Solving time step 0, time = 0

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.92322e-16 < 1e-09
Double norm = 3.08022
  Nonlinear solver converged, step 0, residual reduction 8.93858e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 8.28397e-16 < 1e-09
Single norm = 3.08073
Error norm = 0.00128728
Local relative error = 0.000417849
Global relative error = 0.00417849
old delta t = 0.1
The global growth/shrink factor is: 239.321
The local growth/shrink factor is: 48.9204
delta t is constrained by max_growth
new delta t = 0.112
|U(0.1)|= 1.11633
Advancing timestep

 Solving time step 1, time = 0.1

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 7.10284e-16 < 1e-09
Double norm = 3.18331
  Nonlinear solver converged, step 0, residual reduction 1.26636e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 8.84037e-16 < 1e-09
Single norm = 3.18403
Error norm = 0.00156781
Local relative error = 0.000492398
Global relative error = 0.00439641
old delta t = 0.112
The global growth/shrink factor is: 227.458
The local growth/shrink factor is: 45.0653
delta t is constrained by max_growth
new delta t = 0.12544
|U(0.212)|= 1.35075
Advancing timestep

 Solving time step 2, time = 0.212

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 6.02586e-16 < 1e-09
Double norm = 3.31174
  Nonlinear solver converged, step 0, residual reduction 6.69829e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 2.36797e-16 < 1e-09
Single norm = 3.31273
Error norm = 0.00190279
Local relative error = 0.000574385
Global relative error = 0.00457897
old delta t = 0.12544
The global growth/shrink factor is: 218.39
The local growth/shrink factor is: 41.7252
delta t is constrained by max_growth
new delta t = 0.140493
|U(0.33744)|= 1.67949
Advancing timestep

 Solving time step 3, time = 0.33744

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 4.55856e-17 < 1e-09
Double norm = 3.468
  Nonlinear solver converged, step 0, residual reduction 8.46901e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 9.05589e-16 < 1e-09
Single norm = 3.46933
Error norm = 0.0023003
Local relative error = 0.000663037
Global relative error = 0.00471937
old delta t = 0.140493
The global growth/shrink factor is: 211.893
The local growth/shrink factor is: 38.8357
delta t is constrained by max_growth
new delta t = 0.157352
|U(0.477933)|= 2.08154
Advancing timestep

 Solving time step 4, time = 0.477933

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 5.06191e-16 < 1e-09
Double norm = 3.65407
  Nonlinear solver converged, step 0, residual reduction 6.13537e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 3.55934e-16 < 1e-09
Single norm = 3.65582
Error norm = 0.0027687
Local relative error = 0.000757338
Global relative error = 0.00481302
old delta t = 0.157352
The global growth/shrink factor is: 207.77
The local growth/shrink factor is: 36.3375
delta t is constrained by max_growth
new delta t = 0.176234
|U(0.635285)|= 2.54376
Advancing timestep

 Solving time step 5, time = 0.635285

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 9.4768e-16 < 1e-09
Double norm = 3.87129
  Nonlinear solver converged, step 0, residual reduction 1.05274e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 1.0905e-15 < 1e-09
Single norm = 3.87356
Error norm = 0.00331621
Local relative error = 0.000856113
Global relative error = 0.00485782
old delta t = 0.176234
The global growth/shrink factor is: 205.854
The local growth/shrink factor is: 34.177
delta t is constrained by max_growth
new delta t = 0.197382
|U(0.811519)|= 3.05853
Advancing timestep

 Solving time step 6, time = 0.811519

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 4.65092e-16 < 1e-09
Double norm = 4.1203
  Nonlinear solver converged, step 0, residual reduction 4.79933e-17 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 6.53988e-16 < 1e-09
Single norm = 4.12317
Error norm = 0.00395034
Local relative error = 0.000958082
Global relative error = 0.00485394
old delta t = 0.197382
The global growth/shrink factor is: 206.018
The local growth/shrink factor is: 32.3072
delta t is constrained by max_growth
new delta t = 0.221068
|U(1.0089)|= 3.62108
Advancing timestep

 Solving time step 7, time = 1.0089

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.58181e-16 < 1e-09
Double norm = 4.40092
  Nonlinear solver converged, step 0, residual reduction 3.20932e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 1.44936e-16 < 1e-09
Single norm = 4.40451
Error norm = 0.00467711
Local relative error = 0.00106189
Global relative error = 0.00480346
old delta t = 0.221068
The global growth/shrink factor is: 208.183
The local growth/shrink factor is: 30.6874
delta t is constrained by max_growth
new delta t = 0.247596
|U(1.22997)|= 4.2278
Advancing timestep

 Solving time step 8, time = 1.22997

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 1.69811e-16 < 1e-09
Double norm = 4.71218
  Nonlinear solver converged, step 0, residual reduction 4.94396e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 6.144e-16 < 1e-09
Single norm = 4.71658
Error norm = 0.00550003
Local relative error = 0.00116611
Global relative error = 0.00470971
old delta t = 0.247596
The global growth/shrink factor is: 212.327
The local growth/shrink factor is: 29.284
delta t is constrained by max_growth
new delta t = 0.277308
|U(1.47757)|= 4.8753
Advancing timestep

 Solving time step 9, time = 1.47757

 === Computing adaptive timestep ===
  Nonlinear solver converged, step 0, residual reduction 7.55333e-16 < 1e-09
Double norm = 5.05222
  Nonlinear solver converged, step 0, residual reduction 7.59955e-16 < 1e-09
  Nonlinear solver converged, step 0, residual reduction 2.75131e-16 < 1e-09
Single norm = 5.05754
Error norm = 0.0064188
Local relative error = 0.00126915
Global relative error = 0.0045767
old delta t = 0.277308
The global growth/shrink factor is: 218.498
The local growth/shrink factor is: 28.07
delta t is constrained by max_growth
new delta t = 0.310585
|U(1.75487)|= 5.55978
Advancing timestep

The computed QoI 0 is 0.24932406066164053
The computed QoI 1 is 2.5421286435672119

Solving the adjoint problems.
Setting adjoint initial conditions Z(1.7548735069535084)
|Z0(1.7548735069535084)|= 1

|Z1(1.7548735069535084)|= 0

 Solving adjoint time step 0, time = 1.7548735069535084
|U(1.7548735069535084)|= 5.5597817470095023
|U(1.6162195690809991)|= 5.2227225913862583
Saving adjoint and retrieving primal solutions at time t=1.6162195690809991
|Z0(1.4775656312084897)|= 0.52714277783603058

|Z1(1.4775656312084897)|= 0.26803536445142789

 Solving adjoint time step 1, time = 1.4775656312084897
|U(1.4775656312084897)|= 4.8753000036749743
|U(1.3389116933359804)|= 4.5557169985004684
Saving adjoint and retrieving primal solutions at time t=1.3537674723937492
|Z0(1.2299693135790086)|= 0.085120829331890482

|Z1(1.2299693135790086)|= 0.30479700354857892

 Solving adjoint time step 2, time = 1.2299693135790086
|U(1.2299693135790086)|= 4.2278011018084714
|U(1.1061711547642681)|= 3.9276118455968652
Saving adjoint and retrieving primal solutions at time t=1.1194352432087045
|Z0(1.0089011728384003)|= 0.015691840061529811

|Z1(1.0089011728384003)|= 0.3105712042530332

 Solving adjoint time step 3, time = 1.0089011728384003
|U(1.0089011728384003)|= 3.6210787050559499
|U(0.89836710246809615)|= 3.341951147192225
Saving adjoint and retrieving primal solutions at time t=0.91021003857920024
|Z0(0.81151890432000018)|= 0.0032817876666856086

|Z1(0.81151890432000018)|= 0.31160331107229816

 Solving adjoint time step 4, time = 0.81151890432000018
|U(0.81151890432000018)|= 3.0585320644998721
|U(0.71282777006080011)|= 2.8021388853764262
Saving adjoint and retrieving primal solutions at time t=0.7234018201600001
|Z0(0.63528473600000002)|= 0.00077371056468026299

|Z1(0.63528473600000002)|= 0.31181190031897216

 Solving adjoint time step 5, time = 0.63528473600000002
|U(0.63528473600000002)|= 2.543759970717383
|U(0.54716765183999994)|= 2.3121900921206135
Saving adjoint and retrieving primal solutions at time t=0.55660876800000003
|Z0(0.47793279999999994)|= 0.00020431155391876837

|Z1(0.47793279999999994)|= 0.31185925552612093

 Solving adjoint time step 6, time = 0.47793279999999994
|U(0.47793279999999994)|= 2.0815385167141343
|U(0.39925683199999989)|= 1.8779985387409239
Saving adjoint and retrieving primal solutions at time t=0.40768639999999989
|Z0(0.33743999999999985)|= 6.0043832595599244e-05

|Z1(0.33743999999999985)|= 0.31187125383960418

 Solving adjoint time step 7, time = 0.33743999999999985
|U(0.33743999999999985)|= 1.6794923909523405
|U(0.26719359999999981)|= 1.5094758519366982
Saving adjoint and retrieving primal solutions at time t=0.27471999999999985
|Z0(0.21199999999999986)|= 1.9513594998847448e-05

|Z1(0.21199999999999986)|= 0.31187462461784737

 Solving adjoint time step 8, time = 0.21199999999999986
|U(0.21199999999999986)|= 1.350745356154194
|U(0.14927999999999986)|= 1.2234740927197323
Saving adjoint and retrieving primal solutions at time t=0.15599999999999983
|Z0(0.099999999999999811)|= 6.9689416041385094e-06

|Z1(0.099999999999999811)|= 0.3118756679190276

 Solving adjoint time step 9, time = 0.099999999999999811
|U(0.099999999999999811)|= 1.1163303097816257
|U(0.043999999999999789)|= 1.0439877643180528
Saving adjoint and retrieving primal solutions at time t=0.049999999999999808
|Z0(-1.9428902930940239e-16)|= 2.718164039090695e-06

|Z1(-1.9428902930940239e-16)|= 0.31187602144344273

Computing the error estimate using the Adjoint Refinement Error Estimator

Retrieved, time = -1.9428902930940239e-16
|U(-1.9428902930940239e-16)|= 1
|U_old(-1.9428902930940239e-16)|= 1
|Z0(-1.9428902930940239e-16)|= 2.718164039090695e-06

|Z1(-1.9428902930940239e-16)|= 0.31187602144344273

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.099999999999999811
|U(0.099999999999999811)|= 1.1163303097816257
|U_old(0.099999999999999811)|= 1.0439877643180528
|Z0(0.099999999999999811)|= 6.9689416041385094e-06

|Z1(0.099999999999999811)|= 0.3118756679190276

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.21199999999999983
|U(0.21199999999999983)|= 1.350745356154194
|U_old(0.21199999999999983)|= 1.2234740927197323
|Z0(0.21199999999999983)|= 1.9513594998847448e-05

|Z1(0.21199999999999983)|= 0.31187462461784737

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.33743999999999991
|U(0.33743999999999991)|= 1.6794923909523405
|U_old(0.33743999999999991)|= 1.5094758519366982
|Z0(0.33743999999999991)|= 6.0043832595599244e-05

|Z1(0.33743999999999991)|= 0.31187125383960418

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.47793279999999994
|U(0.47793279999999994)|= 2.0815385167141343
|U_old(0.47793279999999994)|= 1.8779985387409239
|Z0(0.47793279999999994)|= 0.00020431155391876837

|Z1(0.47793279999999994)|= 0.31185925552612093

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.63528473600000002
|U(0.63528473600000002)|= 2.543759970717383
|U_old(0.63528473600000002)|= 2.3121900921206135
|Z0(0.63528473600000002)|= 0.00077371056468026299

|Z1(0.63528473600000002)|= 0.31181190031897216

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 0.81151890432000007
|U(0.81151890432000007)|= 3.0585320644998721
|U_old(0.81151890432000007)|= 2.8021388853764262
|Z0(0.81151890432000007)|= 0.0032817876666856086

|Z1(0.81151890432000007)|= 0.31160331107229816

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.0089011728384003
|U(1.0089011728384003)|= 3.6210787050559499
|U_old(1.0089011728384003)|= 3.341951147192225
|Z0(1.0089011728384003)|= 0.015691840061529811

|Z1(1.0089011728384003)|= 0.3105712042530332

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.2299693135790084
|U(1.2299693135790084)|= 4.2278011018084714
|U_old(1.2299693135790084)|= 3.9276118455968652
|Z0(1.2299693135790084)|= 0.085120829331890482

|Z1(1.2299693135790084)|= 0.30479700354857892

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.4775656312084895
|U(1.4775656312084895)|= 4.8753000036749743
|U_old(1.4775656312084895)|= 4.5557169985004684
|Z0(1.4775656312084895)|= 0.52714277783603058

|Z1(1.4775656312084895)|= 0.26803536445142789

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

The flux QoI 0 is: 0

The flux QoI 1 is: 0

Retrieved, time = 1.7548735069535084
|U(1.7548735069535084)|= 5.5597817470095023
|U_old(1.7548735069535084)|= 5.2227225913862583
|Z0(1.7548735069535084)|= 1

|Z1(1.7548735069535084)|= 0

Time integrated error estimate for QoI 0: -0.75139371165754232
Time integrated error estimate for QoI 1: -0.70905030091469889

 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 13:55:23 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 ----------------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.117004, Active time=0.068443                                                       |
 ----------------------------------------------------------------------------------------------------------------------
| Event                                   nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                                    w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|----------------------------------------------------------------------------------------------------------------------|
|                                                                                                                      |
|                                                                                                                      |
| DefaultCoupling                                                                                                      |
|   operator()                            4          0.0000      0.000001    0.0000      0.000001    0.01     0.01     |
|                                                                                                                      |
| DofMap                                                                                                               |
|   add_neighbors_to_send_list()          1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_constraint_matrix()             560        0.0003      0.000000    0.0003      0.000000    0.37     0.37     |
|   build_sparsity()                      1          0.0000      0.000023    0.0000      0.000028    0.03     0.04     |
|   cnstrn_elem_mat_vec()                 120        0.0020      0.000017    0.0020      0.000017    2.96     2.96     |
|   constrain_elem_matrix()               80         0.0001      0.000001    0.0001      0.000001    0.13     0.13     |
|   constrain_elem_vector()               280        0.0001      0.000000    0.0001      0.000000    0.14     0.14     |
|   create_dof_constraints()              1          0.0001      0.000110    0.0001      0.000115    0.16     0.17     |
|   distribute_dofs()                     1          0.0000      0.000014    0.0000      0.000041    0.02     0.06     |
|   dof_indices()                         2844       0.0006      0.000000    0.0006      0.000000    0.81     0.81     |
|   enforce_adjoint_constraints_exactly() 118        0.0003      0.000003    0.0003      0.000003    0.46     0.46     |
|   enforce_constraints_exactly()         92         0.0018      0.000019    0.0018      0.000019    2.60     2.60     |
|   prepare_send_list()                   2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                              1          0.0000      0.000027    0.0000      0.000027    0.04     0.04     |
|                                                                                                                      |
| EquationSystems                                                                                                      |
|   read()                                63         0.0004      0.000006    0.0004      0.000006    0.56     0.56     |
|   update()                              63         0.0001      0.000001    0.0001      0.000001    0.12     0.12     |
|   write()                               43         0.0223      0.000518    0.0223      0.000518    32.55    32.55    |
|                                                                                                                      |
| FE                                                                                                                   |
|   compute_shape_functions()             1416       0.0058      0.000004    0.0058      0.000004    8.47     8.47     |
|   init_shape_functions()                354        0.0034      0.000010    0.0034      0.000010    4.96     4.96     |
|                                                                                                                      |
| FEMSystem                                                                                                            |
|   assemble_qoi()                        40         0.0010      0.000024    0.0033      0.000082    1.42     4.81     |
|   assemble_qoi_derivative()             20         0.0009      0.000043    0.0021      0.000107    1.25     3.13     |
|   assembly()                            30         0.0023      0.000075    0.0062      0.000206    3.29     9.05     |
|   assembly(get_jacobian)                20         0.0015      0.000077    0.0029      0.000145    2.26     4.23     |
|   assembly(get_residual)                147        0.0063      0.000043    0.0152      0.000104    9.17     22.28    |
|                                                                                                                      |
| FEMap                                                                                                                |
|   compute_affine_map()                  1416       0.0024      0.000002    0.0024      0.000002    3.46     3.46     |
|   init_reference_to_physical_map()      354        0.0039      0.000011    0.0039      0.000011    5.71     5.71     |
|   inverse_map()                         273        0.0001      0.000000    0.0001      0.000000    0.19     0.19     |
|                                                                                                                      |
| GenericProjector                                                                                                     |
|   project                               2          0.0001      0.000039    0.0001      0.000051    0.11     0.15     |
|   project_edges                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_interiors                     2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_sides                         2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   project_vertices                      2          0.0000      0.000008    0.0000      0.000011    0.02     0.03     |
|                                                                                                                      |
| ImplicitSystem                                                                                                       |
|   adjoint_solve()                       20         0.0001      0.000007    0.0064      0.000318    0.20     9.31     |
|                                                                                                                      |
| Mesh                                                                                                                 |
|   find_neighbors()                      1          0.0000      0.000035    0.0000      0.000035    0.05     0.05     |
|   renumber_nodes_and_elem()             2          0.0000      0.000003    0.0000      0.000003    0.01     0.01     |
|                                                                                                                      |
| MeshBase                                                                                                             |
|   prepare_for_use()                     1          0.0000      0.000017    0.0001      0.000060    0.02     0.09     |
|                                                                                                                      |
| MeshCommunication                                                                                                    |
|   assign_global_indices()               106        0.0068      0.000064    0.0068      0.000064    9.98     9.98     |
|                                                                                                                      |
| MeshTools::Generation                                                                                                |
|   build_cube()                          1          0.0000      0.000041    0.0001      0.000101    0.06     0.15     |
|                                                                                                                      |
| NewtonSolver                                                                                                         |
|   solve()                               30         0.0009      0.000031    0.0128      0.000425    1.35     18.65    |
|                                                                                                                      |
| Partitioner                                                                                                          |
|   single_partition_range()              1          0.0000      0.000002    0.0000      0.000002    0.00     0.00     |
|                                                                                                                      |
| PetscLinearSolver                                                                                                    |
|   solve()                               70         0.0019      0.000028    0.0019      0.000028    2.82     2.82     |
|                                                                                                                      |
| System                                                                                                               |
|   calculate_norm()                      127        0.0028      0.000022    0.0036      0.000028    4.16     5.20     |
|   project_fem_vector()                  2          0.0001      0.000028    0.0002      0.000100    0.08     0.29     |
|   project_vector(FunctionBase)          2          0.0000      0.000000    0.0002      0.000100    0.00     0.29     |
 ----------------------------------------------------------------------------------------------------------------------
| Totals:                                 8717       0.0684                                          100.00            |
 ----------------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example adjoints_ex7:
*   ./example-opt n_timesteps=10 timesolver_tolerance=1.0 timesolver_upper_tolerance=1.2 solution_history_type=file
***************************************************************
</pre>
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